Dimension of <xn,tn|xn-1,tn-1>

[einstein1921]

HI! Everyone!I have a problem! I read sakurai's <modern quantum mechanics>.It reads the dimension of <xn,tn|xn-1,tn-1> is 1/length.I DON'T understand!would you like to give me some explanations? thank you!

 

[Simon Bridge]

What don't you understand - it's saying that if you did a dimensional analysis on that thing it would come up with 1/L

Note - you can write in the subscripts in two ways:

<x_n,t_n|x_n-1,t_n-1>

or

$\langle x_n , t_n \mid x_{n-1}, t_{n-1} \rangle$

the second one is best. (assuming you meant the subscripts...)
hit the "quote" button at the bottom of this reply to see what I did.

 

[einstein1921]

What don't you understand - it's saying that if you did a dimensional analysis on that thing it would come up with 1/L

Note - you can write in the subscripts in two ways:

<x_n,t_n|x_n-1,t_n-1>

or

$\langle x_n , t_n \mid x_{n-1}, t_{n-1} \rangle$

the second one is best. (assuming you meant the subscripts...)
hit the "quote" button at the bottom of this reply to see what I did.

Thank you ,Simon.I don't understand why the dimension is 1/length.Could you please did a dimensional analysis for me?

 

[Simon Bridge]

What does the state vector $| x,t \rangle$ represent?

 

[einstein1921]

What does the state vector $| x,t \rangle$ represent?

at time t,particle localize x! I think dimension is length.so I need help. Thank you!